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随机线性假设的非参数推断及高维应用AI 解读

The Mann–Whitney–Wilcoxon rank sum test is limited to comparison of two groups with univariate responses. In this paper, we introduce a class of stochastic linear hypotheses that addresses these limitations within a nonparametric setting. We formulate hypotheses for simultaneous comparisons of several, multivariate response groups, without modelling the response distributions. Inference is developed based on U‐statistics theory and an exchangeability assumption. The latter…

顺序多元失效时间数据的间隔时间风险回归AI 解读

Sequentially ordered multivariate failure time data are often observed in biomedical studies and inter‐event, or gap, times are often of interest. Generally, standard hazard regression methods cannot be applied to the gap times because of identifiability issues and induced dependent censoring. We propose estimating equations for fitting proportional hazards regression models to the gap times. Model parameters are shown to be consistent and asymptotically normal. Simulation…

We study the profile‐kernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential root‐n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting…

高斯球谐函数上的经验过程AI 解读

We establish weak convergence of the empirical process on the spherical harmonics of a Gaussian random field in the presence of an unknown angular power spectrum. This result suggests various Gaussianity tests with an asymptotic justification. The issue of testing for Gaussianity on isotropic spherical random fields has recently received strong empirical attention in the cosmological literature, in connection with the statistical analysis of cosmic microwave background…

经验似然比置信区域覆盖概率的上界AI 解读

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed.

重尾分布均值的经验似然置信区间AI 解读

Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237–249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the domain of attraction of a stable law with index between 1 and 2. In this article we use a method similar to Qin and Wong [Scand. J. Statist. 23 (1996) 209–219] to derive an empirical-likelihood-based confidence interval for the mean when the…

基于局部 L2 拟合的半参数密度估计AI 解读

This article examines density estimation by combining a parametric approach with a nonparametric factor. The plug-in parametric estimator is seen as a crude estimator of the true density and is adjusted by a nonparametric factor. The nonparametric factor is derived by a criterion called local L2-fitting. A class of estimators that have multiplicative adjustment is provided, including estimators proposed by several authors as special cases, and the asymptotic theories are…

偏倚抽样数据的密度估计AI 解读

The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that depends on the value of the observation. This is an interesting sampling procedure because it favors some observations and neglects others. It is known that biasing does not change rates of nonparametric density estimation, but no results…

充分降维中的预测变量贡献检验AI 解读

We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean function and smoothing is not required. The general approach is based on sufficient dimension reduction, the idea being to replace the predictor vector with a lower-dimensional version without loss of information on the regression. Methodology…

参数维度随样本量增长的非凹惩罚似然AI 解读

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of procedures has an oracle property when the number of parameters is finite. However, in most model selection problems the number of parameters should be large and grow with the sample size. In this paper some asymptotic properties of the…

半参数回归中的一致协变量选择与模型选择后推断AI 解读

This paper presents a model selection technique of estimation in semiparametric regression models of the type $Y_{i}={\beta}^{\prime}\underline{X}_{i}+f(T_{i})+W_{i}$ , i=1,…,n. The parametric and nonparametric components are estimated simultaneously by this procedure. Estimation is based on a collection of finite-dimensional models, using a penalized least squares criterion for selection. We show that by tailoring the penalty terms developed for nonparametric regression to…

一类非高斯平稳过程与随机场的分形维数估计AI 解读

We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R→R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on Rd, d=1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is “fixed domain” (or “infill”) asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat…

错误发现控制的随机过程方法AI 解读

This paper extends the theory of false discovery rates (FDR) pioneered by Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289–300]. We develop a framework in which the False Discovery Proportion (FDP)—the number of false rejections divided by the number of rejections—is treated as a stochastic process. After obtaining the limiting distribution of the process, we demonstrate the validity of a class of procedures for controlling the False Discovery Rate (the…

回归模型中基于鞅变换的拟合优度检验AI 解读

This paper discusses two goodness-of-fit testing problems. The first problem pertains to fitting an error distribution to an assumed nonlinear parametric regression model, while the second pertains to fitting a parametric regression model when the error distribution is unknown. For the first problem the paper contains tests based on a certain martingale type transform of residual empirical processes. The advantage of this transform is that the corresponding tests are…

用于检测稀疏异质混合的 Higher Criticism 检验AI 解读

Higher criticism, or second-level significance testing, is a multiple-comparisons concept mentioned in passing by Tukey. It concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis. Tukey suggested comparing the fraction of observed significances at a given α-level to the expected fraction under the joint null. In fact, he suggested standardizing the difference of the two quantities and forming a…

存在异常值时的协整分析AI 解读

The effects of innovational outliers and additive outliers in cointegrated vector autoregressive models are examined and it is analyzed how outliers can be modelled with dummy variables. A Monte Carlo simulation illustrates that additive outliers are more distortionary than innovational outliers, and misspecified dummies may distort inference on the cointegration rank in finite samples. These findings question the common practice in applied cointegration analyses of…

多元长记忆过程的渐近推断结果AI 解读

In this paper, we extend the well-known Sims, Stock and Watson (SSW) (Sims et al. 1990; Econometrica 56, 113-44), analysis on estimation and testing in vector autoregressive process (VARs) with integer unit roots and deterministic components to a more general set-up where non-stationary fractionally integrated (NFI) processes are considered. In particular, we focus on partial VAR models where the conditioning variables are NFI since this is the only finite-lag VAR model…

利用桥采样估计混合模型与马尔可夫转换模型的边际似然AI 解读

This paper discusses the problem of estimating marginal likelihoods for mixture and Markov switching model. Estimation is based on the method of bridge sampling (Meng and Wong 1996; Statistica Sinica 11, 552-86.) where Markov Chain Monte Carlo (MCMC) draws from the posterior density are combined with an i.i.d. sample from an importance density. The importance density is constructed in an unsupervised manner from the MCMC draws using a mixture of complete data posteriors.…

A computationally simple maximum likelihood procedure for multivariate fractionally integrated time series models is introduced. This allows, e.g., efficient estimation of the memory parameters of fractional models or efficient testing of the hypothesis that two or more series are integrated of the same possibly fractional order. In particular, we show the existence of a local time domain maximum likelihood estimator and its asymptotic normality, and under Gaussianity…

线性检验与平稳性AI 解读

This paper shows that the asymptotic distributions of LM-type linearity tests against Smooth Transition Autoregressive (STAR) models, in the presence of a unit root, are non-standard and using standard χ2 critical values may lead to incorrect inference as the tails of the distribution of tests will be thicker than the χ2. This finding also indicates that one needs to test for stationarity prior to applying linearity tests. Copyright Royal Economic Socciety 2004

误设下均值与方差断点的最小二乘估计及检验AI 解读

In this paper we investigate the consequences of misspecification on the large sample properties of change-point estimators and the validity of tests of the null hypothesis of linearity versus the alternative of a structural break. Specifically this paper concentrates on the interaction of structural breaks in the mean and variance of a time series when either of the two is omitted from the estimation and inference procedures. Our analysis considers the case of a break in…

弱工具变量下的估计：高阶偏误与均方误差近似的准确性AI 解读

In this paper, we consider parameter estimation in a linear simultaneous equations model. It is well known that two-stage least squares (2SLS) estimators may perform poorly when the instruments are weak. In this case 2SLS tends to suffer from the substantial small sample biases. It is also known that LIML and Nagar-type estimators are less biased than 2SLS but suffer from large small sample variability. We construct a bias-corrected version of 2SLS based on the Jackknife…

第一阶段基于分位数回归的两阶段分位数回归AI 解读

We present the asymptotic properties of double-stage quantile regression estimators with random regressors, where the first stage is based on quantile regressions with the same quantile as in the second stage, which ensures robustness of the estimation procedure. We derive invariance properties with respect to the reformulation of the dependent variable. We propose a consistent estimator of the variance--covariance matrix of the new estimator. Finally, we investigate finite…

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